The table below gives values of the functions \(f\) and \(g\) at different values of \(x\). What is \(f(g(1))\) ?

$$ \begin{array}{c|c|c|c} x & 1 & 2 & 3 \\ \hline f(x) & 3 & -6 & 2 \\ g(x) & 2 & 7 & 1 \end{array} $$

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From the table, \(g(1)=2\).

$$ f(g(1)) = f(2) $$

From the table, \(f(2)=\boxed{-6}\).